Abstract : We complete the known results on the local Cauchy problem in Sobolev spaces for the KdV-Burgers equation by proving that this equation is well-posed in $ H^{-1}\R $ with a solution-map that is analytic from $H^{-1}\R $ to $C0,T;H^{-1}\R$ whereas it is ill-posed in $ H^s\R $, as soon as $ s